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Abstract

Fluorescence Correlation Spectroscopy (FCS) yields measurement parameters (number of molecules, diffusion time) that characterize the concentration and kinetics of fluorescent molecules within a supposedly known observation volume. Absolute derivation of concentrations and diffusion constants therefore requires preliminary calibrations of the confocal Point Spread Function with phantom solutions under perfectly controlled environmental conditions. In this paper, we quantify the influence of optical aberrations on single photon FCS and demonstrate a simple Adaptive Optics system for aberration correction. Optical aberrations are gradually introduced by focussing the excitation laser beam at increasing depths in fluorescent solutions with various refractive indices, which leads to drastic depth-dependent bias in the estimated FCS parameters. Aberration correction with a Deformable Mirror stabilizes these parameters within a range of several tens of μm into the solution. We also demonstrate, both theoretically and experimentally, that the molecular brightness scales as the Strehl ratio squared.

ACF recorded in the 70.4 % glycerol solutions, without (left) and with (right) AO. The amplitude of the ACF decreases dramatically with increasing observation depth (from 10 to 45 μm) when the AO is not switched on. The superimposed dark solid lines are the fits performed with Eq. (4).

Aberrations corrected by the DM in the glycerol solutions: spherical aberration amplitudes (a10, open circles) and the residual aberrations (r10, open squares) for the 50% glycerol solution (blue) and for the 70.4% one (red); solid lines are linear fits of the spherical aberration amplitudes.

Comparison of the molecular brightness with the Strehl ratio squared, computed using Eq. (8) (solid lines). Left graph: the ordinate on the vertical axis, CRM/CRM10, is normalized to its value at the reference depth z = 10 μm, and the horizontal axis is the overall RMS amplitude of the corrected aberrations, σwf, in the glycerol solutions (50 % solution in blue and 70.4 % one in red). Right graph: the ordinate on the vertical axis, CRM/CRMa=0 is normalized to its value when no single mode aberration is applied, the horizontal axis is the amplitude of a single Zernike mode (a4: astigmatism in magenta, a10: spherical aberration in green), generated by the DM in an A647 80 nM pure water solution, while other aberrations are corrected.